Posted
by
samzenpus
on Monday February 11, 2013 @04:03PM
from the new-math dept.

First time accepted submitter Ben Rooney writes "Children in the Baltic state of Estonia will learn statistics based less on computation and doing math by hand and more on framing and interpreting problems, and thinking about validation and strategy. From the article: 'Jon McLoone is Content Director for computerbasedmath.org, a project to redefine school math education assuming the use of computers. The company announced a deal Monday with the Estonian Education ministry to trial a self-contained statistics program replacing the more traditional curriculum. “We are re-thinking computer education with the assumption that computers are the tools for computation,” said Mr. McLoone. “Schools are still focused on teaching hand calculating. Computation used to be the bottleneck. The hard part was solving the equations, so that was the skill you had to teach. These days that is the bit that computers can do. What computers can’t do is set up the problem, interpret the problem, think about validation and strategy. That is what we should be teaching and spending less time teaching children to be poor computers rather than good mathematicians.”'"

The US has been focused more on mathematics for as long as I can remember. That's one reason why the US is usually behind China in terms of math, China places a ton of value on turning children into calculators rather than understanding any of the math they're being expected to rote memorize.

I'm not so sure that going the computer route is such a great idea. It's all well and good to use computers and calculators, but if you don't know your times tables and you can't do long division, you're going to be stuck having to have a calculator at all times. Which is more reasonable now than it used to be, but you'd be surprised how much faster it can be to do things on paper sometimes.

Oh, and good luck getting a calculator to tell you what went wrong when a number you get isn't right.

california doesn't focus on math. to graduate high school you need 2 years of math and 3 1/2 years of p.e.

It's not like after learning 2 years worth of math you just forget it instantly. But with P.E., if you stop exercising, your body goes straight back to tubby-land. You are comparing apples and oranges in a most ridiculous way.

I disagree! A year after graduating high school, most people can't do basic arithmetic nearly as proficiently as they did when in school. You get rusty at those skills real fast if you're not using them daily. As for trigonometry, basic calculus and stuff you may have had less than a year learning (Maths until final year was compulsory in my school) that's even worse.

Aside when I sleep I've got a calculator on me at all times. My phone? A calculator. My laptop? A calculator. My iPod? A calculator.

And yes, there's a reason why China is behind the US in terms of math, because, like you said a lot of the value is placed on rote memorization, but that is also the reason why China has lagged behind the US in terms of real innovation.

Oh, and good luck getting a calculator to tell you what went wrong when a number you get isn't right.

Except this is what Estonia is having students learn: what the numbers really mean and how to use them. Which is a more useful skill, to be able to compute the A^2+B^2=C^2 your head or to be able to recognize a right triangle when you see one and be able to use that formula to find out useful information?

What most education systems are doing is teaching kids to memorize formulas and be able to do them with pencil and paper (or in their head) but not telling them when to use it or what the numbers really mean. You can ask most students what the Pythagorean theorem is and they can tell you, but how many of them can actually practically use it?

Except most students will not have a need to do the arithmetic by hand except for very basic problems.

To use a car analogy its a bit like riding a horse. Back in the days before cars and trains, if you needed to travel long distances you had to ride a horse. If you didn't know how to ride a horse you were at a distinct disadvantage compared to someone who could ride a horse. Knowing how to do complex math by hand in today's age is a bit like knowing how to ride a horse today. It might be an interesting

In the US we don't divide the curriculum based on what we think the students will do in the future. Some countries do this however. They may have a pre-college high school separate from a trade oriented high school. In the US though we give the same education to everyone, rich or poor, with educated or uneducated parents alike. So we do want to teach good math and science to everyone, because you can never predict who will need it in the future. Over time the student decides that they can't handle the

A guy who really enjoys history is likely to be thrilled by the prospect of an in-depth class on the political environment of the Italian Renaissance. On the other hand, there's people who couldn't care less about such a subject.

There are people who enjoy Trig or who will use it in their expected careers. Then there are others who simply loathe it and will never use it in their life.

No, ability is primarily driven by effort put into it. I wasn't good at math when I was a kid, I was terrible at reading. I could barely read at all until I was 8, certainly well behind my peers. The logical extension of your view is that I not be required to read or write because it was frustrating.

After many years, I did eventually manage to master reading sufficiently well that I can read without needing to hear the words in my head as I go along and I actually enjoy reading. The parts of my brain respon

The problem is that you rarely, if ever, see somebody that can't do basic arithmetic who is able to understand things well enough to use a calculator. I tutor developmental math students on this stuff, and by and large I don't see very many of them that understand the concepts without being able to perform basic arithmetic. It's far more common for them to get the arithmetic, but be completely unable to do math.

The US has been focused more on mathematics for as long as I can remember. That's one reason why the US is usually behind China in terms of math, China places a ton of value on turning children into calculators rather than understanding any of the math they're being expected to rote memorize.

I'm not so sure that going the computer route is such a great idea. It's all well and good to use computers and calculators, but if you don't know your times tables and you can't do long division, you're going to be stuck having to have a calculator at all times. Which is more reasonable now than it used to be, but you'd be surprised how much faster it can be to do things on paper sometimes.

Oh, and good luck getting a calculator to tell you what went wrong when a number you get isn't right.

The problem is that solving complicated algebraic equations require you to have good mental arithmetic skill, otherwise everything becomes a pain. If the students can't do basic arithmetics quickly, they will find it hard to reason about complex problems. I feel the new approach by Estonia might backfire on them once students reach high school.

My daughter (who now has her own kids) was taught basic algebra at an Aussie HS using a spreadsheet, it was the teacher's own idea and it worked a treat. I think it worked so well because she was doing rather than just seeing or hearing.

A lot of kids have trouble with algebra because they don't get the basic concept of variables and references, they do understand those concepts in general they just don't link it to algebra. I had the same problem teaching grown ups C pointers many years ago, in a lab cla

Much beyond simple mathematics (addition subtraction multiplication and division) is seldom encountered in the lives of many people.However people working in the trades (electricians, carpenters, mechanics) usually need a little more.

But your first sentence seem to contain an internal contradiction. You claim china speed too much time on memorization and not enoughtime on understanding. Yet you state that China leads the US in this regard.

However people working in the trades (electricians, carpenters, mechanics) usually need a little more.

What do electricians need to calculate beyond the basic operations? Working out how much cable to go from point X to Y via Z? Addition. What current is necessary for a given power? Division. I doubt carpenters use integration to determine the volume of newel posts, and as for mechanics most of them can barely add the bill up correctly.

So, you've never heard of the cos phi? Or a complex impedance? Electricity is reasonably dead simple if you're only dealing with DC voltages or currents but once you're dealing with AC you'd better have a basic understanding of trig, complex numbers and exponentials.

Oh, and good luck getting a calculator to tell you what went wrong when a number you get isn't right.

This.

When I was in graduate school I was TA for a chem lab. For one of the quizzes, a student said he'd forgotten his calculator and asked to borrow mine.

His: TI.
Mine: HP.
Grading him extra points off when he came back with the answer "1.000" for a concentration problem: Priceless.

He knew how to operate his calculator, probably. He didn't know how to operate mine ( "number enter number enter divide" is different than "number enter number divide"). And he demonstrated a complete lack of feeling for the concentration of hydrogen ions in a solution. Unfortunately, it was the latter that he was supposed to learn in this class, not the former. By going with the answer 1.0 "because the calculator said so", he screwed himself and showed a failure to grasp the course material. Had he not been dependent on the calculator, he could have realized that "1.0" is a really really really strong acid, and the buffer he was calculating would never be that strong. The correct answer was five orders of magnitude away, at least.

The sad part of today's "find a calculator" climate is that people have lost the ability to ballpark anything.

There's no contradiction there. There is some declarative knowledge that you have to learn in any field. If you don't know your times tables, it's difficult to function at all in society where math is being used. It was expected of myself and my classmates to be permitted to move to fifth grade that we know our times tables up to 10x10.

In fact without some declarative knowledge you'll never advance very far. It's declarative because there isn't really anything to understand other than the fact that it is wh

I agree w/ 'both', but one does have to prioritize. Things like binary arithmetic and Boolean algebra are simple enough to be taught in, say, 5th grade. From then on, they can start learning things progressively, such as the truth tables of various circuits, even while in Physics, they start getting introduced to electrical concepts. So that by the time they're out of high school, they have a good sense of how to design or program things.

rote memorization of addition tables and multiplication tables would still be important to understanding the results. And also shortcuts. Otherwise, the concept of 43+43 is the process of counting to 86. Not knowing you can add the digits separately and the concept of a carry digit would seriously hinder people.

If you use an abacus, a very ancient device, these ideas come naturally. Even though the abacus is just a calculator it does not hide things from the user. With a digital calculator you essentially have a function that turns two numbers into a third number. Similarly with slide rules, you could do multiplication by using logarithms and it wasn't hidden from you. Further with the slide rule you got a very good feeling for the scale of the inputs and outputs, how you got more precision on one end and low

1. When's the last time you were more than 10 feet from a computer? How often do you think it's going to be in the next generation.2. I'd rather have graduates who can do calculus with a computer, than those that can fuddle and almost do Alegbra without. That may be the choice we have to make.3. Do you seriously think they're going to teach by saying "the computer always solves any problem", without broaching the mechanics at all?

Sentence 1 of your reply has no relationship to sentence 2, so I'm going to argue against what I imagine your point to be. This might be pointless:

If they aren't doing algebra, its going because they're stuck algorithmic bullshit like memorizing the quadratic equation, then they'll never make it to calculus, which was exactly my point.

No one needs to waste time learning to do square-roots by hand. No one needs to memorize multiplication tables. No one needs spend a ton of time on the algorithmic execution of concepts in math, except those developing re-usable algorithms to that effect(mathematicians and programmers). I can't remember the last time I did long-division by hand(except of course, of polynomials, but that hardly counts). Either precision matters little enough that I can approximate, or precision and accuracy matter enough that I wouldn't want anything but a computer to do it.

So basically this generation is the last who needs to know how to do math?

The next one just needs to know how to punch it into a computer and hope the answer is right?

That is, well, stupid.

For one thing, this would make financial fraud, well, much more widespread than it already is. Being able to tell whether a total is even approximately correct has repeatedly saved me money, as well as being able to determine how much change I should get.

That really depends on how you define algebra and calculus. When I was in university, I did quite well at linear algebra, but didn't do as well at calculus. I also knew a lot of people who had the exact opposite problem. For some people, certain skills are just easy to pick up, for other people, it will be completely different skill. Though I agree with you that it's a false dichotomy. People who aren't able to do basic arithmetic won't be very good at doing calculus.

Back when I worked retail management as a starving student (admitted a couple decades ago, now) we had to fire a girl because she didn't know how to make change. Like the cash register reads 37 cents, now which coins to you hand to a customer? She simply could not figure it out. Even after trying to teach her to count up, she simply couldn't add numbers fast enough. I'm sure she's probably a CEO or accountant now.

So we're back to the old calculator debate, but in new clothes. When I was at school the argument was all about whether to use calculators or not. For most of my school career, I survived without recourse to a calculator. I had a calculator, but I never used it, because the course materials were always designed in such a way that we didn't need one. We didn't need to "calculate" the final answer, we just reduced equations, and that led us to exactly what the quote in the summary calls for: mathematician

It is about time that schools embraced calculators and computers when it comes to math. When it comes to having a competitive edge and actually DOING something with math, the question isn't if you can do 123123.12 x 213123 / 23423.28 in your head, it is about learning to apply mathematical principles in the real world. You quite simply cannot get a job simply because you are good at doing addition, multiplication, subtraction and division. 100 years ago before the advent of the computer that might be true. Today though? Everyone has a calculator on them nearly all the time. The question is not if you can accurately calculate how much that $7.99 shirt is going to be if it is taxed at 7%, but how to plug in the numbers for that. The question isn't manually computing how to do a PageRank algorithm, but understanding the logic behind that (and improving it!).

100 years ago before the advent of the computer that might be true. Today though?

A large part of the modern educational system is geared precisely toward that. We are easily the best prepared 1913 workforce the world has ever seen. Our 10000 man factories will be staffed by fully qualified drones, our draftsmen are fast and precise when hand drawing blueprints... The more you think about it, the truer it is. The bell rings, just like a factory whistle. Rows of desks just like rows of (hand/human operated) machines on the factory floor. Not much has changed in over a century.

Yep. Looking back at my elementary school/middle school years that rang especially true. I'm not -that- old (graduated HS in 2008) but the stuff I learned was already obsolete by the time I learned it.

For example, in Kindergarten I learned print handwriting. In first grade I learned D'Nealian (basically a bastardized version of cursive, not quite print and not quite cursive) by third grade teachers required that everything should be written in cursive. The idea was that somehow, despite the fact that computers were everywhere and few people actually used cursive that it was a required skill to learn and that we'd be using it the rest of our lives. Wrong. Aside from a time from 3rd to 5th grade when teachers required it, I never used cursive, it was really a waste of time.

There's a whole host of useless things I learned, each with a rationale that we'd be using this "skill" the rest of our lives. Which might be true if I lived in 1950, but I don't. I remember at some point we were forced to keep a pen-and-paper agenda and my request to use my PDA to keep track of things (I mean, nothing fancy just my dad's hand-me-down monochrome Palm Pilot) and that request was flatly denied. There were all sorts of things that I could have been (and should have been!) taught in elementary/middle school, things like computer programming, basic electronics, etc. but those were overshadowed by much more "important" things such as learning to write in cursive...

I'm glad to see this mentality that calculators don't exist banished from classrooms.

The question is not if you can accurately calculate how much that $7.99 shirt is going to be if it is taxed at 7%

You're right, that isn't the question. The real question is how to save money on your shopping trip. So, when you're in the store and want to know what the better purchase is, the box of 14 for $12.95 or the box of 32 for $29.99, I assume you never choose incorrectly for any of the similar selection of 20 items your picking up this trip since you're always using your handy dandy calculator!

Since I never see anybody using a calculator when I'm out shopping, I'm going to go out on a limb and guess that bein

If they don't print the per-unit costs on the label, then when you think I'm looking at my shopping list on my phone, I'm actually using a calculator to figure out which of those is the better deal. Usually, though, the per-unit costs are printed on the label on the shelf.

In Estonia, it's explicitly the law that they must carry the per-kg/per-l price on the shelf tag or item itself.

Which reminds me, I have some photos to send to the consumer protection board - those shelf tags can sometimes be hilariously wrong. Having said that, maybe I should send them to the supermarkets first, and see if they reward me with a free supermarket sweep. Blackmail's not below me, when there's the possibility of free food - do I look stupid?!?!

My mum was out shopping once. She bought two or three things in a shop, at £x.99, £y.99 and £z.95. There was a fault in the electrics and the cash register was out. The shop assistant attempt to calculate the total by long addition and was taking ages. My mum was a maths teacher. She showed her the "divide-and-conquer" algorithm for adding multi-digit numbers ((x+1) + (y+1) + (z+1)) - (0.01+0.01+0.05). The woman behind the counter was very grateful, because she'd never been shown thi

We have moved quite a bit forward from calculators. The question now is not whether to teach arithmetic, more like whether to teach calculus and equation systems, or just use a symbolic program. I still think it's useful to at least learn how they work, but cutting back on doing repeated exercises might be a good idea.

We need both. If you can't calculate by hand you don't actually learn many vital concepts. Ie, how does a computer do division? The same way a person does division. The person who designed the chip to do the division is unable to do so without first knowing how to do it the long way. Even if you're not designing a chip you still learn some fundamental concepts by understanding the process.

Do you even understand what 7% tax means if all you know is how to plug in numbers into a calculator? If you just

I think you are missing what Estonian schools are teaching. They aren't going to be throwing away math instruction but they are going to be talking about what the numbers mean. For example, they will talk about what a 7% tax is, talk about what are the expected numbers, etc.

And no, its not "dysfunctional" to get your algorithms and just put them in your program, its called efficiency. Why re-invent the wheel (and introduce potential bugs) by re-coding something that is already done (and tested)? I mean,

And no, its not "dysfunctional" to get your algorithms and just put them in your program, its called efficiency. Why re-invent the wheel (and introduce potential bugs) by re-coding something that is already done (and tested)? I mean, sure a programmer could spend 85% of their time re-coding existing code, and the remainder working on new stuff, or they could just take existing, working code and focus on adding the new stuff.

[...]

Um, have you even been in an American school? The entire program right now is to make factory floor workers! We focus on obsolete gruntwork rather than focusing on the big picture. We prepare students for life in 1913 rather than 2013. We ignore many technological advancements for the sake of a "complete" education. We waste time teaching students print, cursive and keyboarding rather than just print and keyboarding. We waste time trying to cram in dates and years rather than teaching the principles behind history so we can learn from it. Its the same with math, we can either focus on the gruntwork and spend 95% of our time teaching kids how to do long division and things of that nature, and only 5% discussing the principles behind it. Or we can spend 95% of our time discussing the principles behind it and only 5% discussing the gruntwork behind it.
The idea of the human calculator and the human encyclopedia is over. Real-world success isn't being able to quote dates or do multiplication in your head, its applying those concepts to the world around us. Its not knowing 400 digits of Pi but being able to use Pi to model the world.

Well then let me ask: have you ever been inside a non-US school? Because it is not just a choice between mindless rote repetition on one hand and throwing all the paper away and working on a computer on the other. You can learn the fundamentals of how numbers and probabilities and algebra and geometry work meaningfully, and once you've learned it, you can apply it.

If you object to teaching the fundamentals, and instead focus on plugging numbers into a precoded algorithm, then you are indeed teaching for 2

Especially since it's sepcifically statistics that's involved in the push.

Back in the last half of the 1960s hand calculators were just becoming available and affordable. There was a bunch of pressure to ban them and maintain the old curricula, with hand computation everywhere.

The big mover to calculators was the statistics department. That's because the arithmetic involved in statistics calculations is long and tedius. Assignments could only be toys. Computing a chi-square test using pencils and paper was a group term project. So the students had to eat a semester of theory and have hands-on experience of doing the work ONCE.

With hand calculators a chi-square on a reasonably-sized dataset could be done for a daily assignment. The students could move on from crunching and actually SEE the tools work, getting a "feel" for the processes. That, in turn, meant they could learn MORE tools in the same time.

With computers the computation can be faster than the delay can be perceived, so students can apply another factor-of-many multiplier to how much of the subject they can cover and how well they can comprehend it.

There are some subjects where the number of computations small enough that manual arithmetic is occasionally useful at a professional level, complex enough that understanding all the steps to set it up is important, and powerful enough that a small number of complex computations does something important - rather than bogging you down in an impossibly large number of simple, repetitive, and error-prone steps. Statistics is NOT one of these subjects.

I mean really - back when I took Maths 'O' levels you weren't allowed calculators in the exam room. I'd do the maths and then check my answer on the slipstick. Slide rules aren't great for accuracy, but ok for quick checks.

I think after establishing a base of being able to do simple arithmetic with adequate competency, there is diminishing returns in making people better human calculators. It's not that I don;t think this is a useful skill, but rather that I feel the lost opportunity cost from not teaching them more useful things like how to think about problem solving is not a good tradeoff.

We make kids do the same kinds of math problems over and over again. I can barely remember how to do long division nowadays (although I could probably figure it out fairly quickly). Is the reason I can figure it out based on the fact that I was forced to do it over and over again as a kids? Not really. I can figure it out because I know what it is that long division was meant to achieve. I can apply what I learned alter on to rederive long division, although memory can speed this up a a little bit.

Knowing how to think is more versatile than memory. Knowing how to think allows you to do more than just long division. In the same way that we wouldn't dream of making kids use books of logarithms in light of how much better using a calculator is, why not let them use calculators for basic arithmetic, once they've mastered it (and by mastered I don't mean do lightning fast, but just reliably). All the time saved by using calculators means that we can teach them how to do new things sooner.

In my experience, this is the case for everything, from primary school through to university. Memorisation is the way that stuff is taught throughout education, which makes sense - it's easy, makes marking and standardised testing easier, and it makes people seem competent. It also ignores the fact that learning the concepts and being able to apply them is so much more important.

I have to admit my bias for the former, but teaching rote calculation in one's head has some value, if only as mental calisthenics. That said, I applaud the Estonian school system for getting more reality based, unlike so many school systems here in the USA.

Full disclosure: I'm half Estonian, do some math in my head, and I still write in cursive, occasionally. Keeps the kids from understanding it.:)

I'm not sure I can trust a WSJ write-up. Perhaps err.ee have covered it, but I don't see anything resembling that presently. I also don't know anyone with kids of school age here, so can't verify what the real implications are.Certainly, being able to use the commonly-available equipment in order to perform tedious calculations is a more useful skill than being able to manually perform those calculations most of the time. However, the ability to detect an significant error in those calculations is vital, wh